You need to keep your DD completely away from this toxic 'friend'.
If the mother contacts you again, listen, then tell her you hope she has found appropriate mental health care for her DD, and put the phone down.
Do not start in on the hours left home, or the shows the daughter watches. Do not engage with this drama-loving women and her daughter.
The DD's inadequate social and emotional development are not your problems to fix.
Self harm takes off like wildfire in schools. It is contagious, and it is far worse since social media became such a big part of tweens' lives.
Your DD is not the problem here.
11, 12, 13 - very difficult years for girls socially. The issues of jealousy, fear of rejection and abandonment, insecurity/anxiety and the burgeoning herd instinct (based on evolution, where the weakest is cruelly isolated from the rest) make for a very fraught and occasionally dangerous social landscape.
Girls with mothers who live for drama have a much harder time than others in these years.
You need to model keeping yourself well apart from other people's problems here. Tell your DD as many times as needed that she must not get sucked into the drama.